Toward a curriculum of verbs

“Verbs make sentences go. They are where and how a sentence lives,” writes Mark Tredinnick in The Little Red Writing Book. Verbs do the same for mathematics. They “make maths go”. They are how mathematics happens. Verbs are where mathematics comes alive.

Curriculum documents are full of verbs. Here are the top ten occurring in the AC:M Years 7-10 content descriptions and the number of occurrences (out of 323 occurrences of 61 different verbs). What do you notice?

use (59), solve (36), interpret (17), describe (14), recognise (12), formulate (10), report (9), apply (8), compare (8), conduct (8)

To me, they lack vitality. They’re prescriptive: use this; solve that. They convey a sense of certainty that you’ll be able to do exactly what’s specified with a known body of knowledge. I’m not disputing their importance, only the undue emphasis placed on these directives.

The proficiencies—understanding, problem solving, reasoning, fluency—were introduced into the Australian Curriculum: Mathematics to emphasise that learning mathematics is more than learning procedures. So how do their verbs stack up? I’ve isolated the verbs that describe student actions within each proficiency. Can you work out which proficiency corresponds to each collection of verbs? (Answers at the bottom of the post.)

develop, analyse, prove, experiment, model, evaluate, explain, infer, justify, generalise, explain, deduce, justify, adapt, transfer, prove, compare, contrast, reflect, explain
develop, practise, consolidate, choose, carry [out], apply, connect, choose, use, recognise, choose, understand, apply, manipulate, find
use, solve, engage, work, plan, apply, find, review, analyse, draw, solve, communicate, justify, identify, formulate, apply, obtain, evaluate, interpret, communicate
build, refine, make [connections], draw [upon], adapt, transfer, cultivate, develop, build, connect, represent, identify, describe, interpret

Better, perhaps. But where’s the invitation to explore, to tinker, to create? Are our students merely patrons being served a prepared meal? Or can they be the chefs, experimenting, tasting and tweaking in the kitchen?

Yes. They can.

How? As teachers, we can start by remembering what it means to play with mathematics, inspired by people like David Butler, Christopher Danielson, Michaela Epstein, Dan Finkel, Annie Perkins, and many more. We can learn from the practices of mathematicians. (Come back in a fortnight for more on this.)

I’d love to curate a list of verbs that are invitations to be curious, creative, imaginative, and playful, and that we can infuse into our students’ mathematical experiences. Here are a few to get us started. What others would you suggest for the list?

consider, try, suppose, explore, imagine, choose, conjecture, claim, question, discover,
convince, suggest, generate, appreciate, argue, experiment, guess, investigate, devise, sketch

In writing this, I realised I’d forgotten about adjectives. Used well, they add zing. Extending the food metaphor, they’re the sharp, lively flavours that make a dish interesting. The adjectives in the AC:M are decidedly functional. So, just for fun, I created a playful prompt generator in the style of [verb] a/an [adjective] [noun]. Here are some suggestions it gave me. I can think of a response to each of them. What about you?

Suggest a cool variable. What makes it cool?
Make a curvy integer. What makes it curvy?
Measure a hard angle. What makes it hard?
Consider a big curve. What makes it big?
Explore a weird square. What makes it weird?
Make a tiny fraction. What makes it tiny?
Construct a surprising triangle. What makes it surprising?
Create an imaginary unit. What makes it imaginary?

Chefs need to understand the properties of foods and how to cook them. But they also need to experiment to discover what works well together and to create new dishes. Similarly, students need to understand the foundational concepts and procedures in mathematics. But they also need opportunities to explore, experiment, and create.

So, the next time you’re crafting a mathematical experience for your students, remember the verbs. Consider their power to ignite curiosity and creativity. Let them bring mathematics to life.

Reasoning, Fluency, Problem Solving, Understanding

Photo by Mohamed Nohassi on Unsplash